On Sunday, 22 December 2013 15:05:27 UTC+1, Pfsszxt wrote: > On 12/20/2013 8:56 AM, firstname.lastname@example.org wrote: > > > To be precise: > > > > > > There is no potentially infinite list of potentially infinite 0/1 > > > sequences, L, with the property that any potentially infinite 0/1 sequence > > > is in L > > > > > > William Hughes > > > > ? Precise? Is "potentially infinite" a well defined > > mathematical term??
Of course. It is a sequence (a_n) of terms a_n the indices n of which surpass any given number but are never complete in that always infinitely many are beyond any given index n. (Actual infinity, the usual infinity notion of set theory, is the same with the exception that set theorists believe that the infinitely many missing terms are "complete" in some sense and can be used such that no term is missing - obviously a contradiction with the axiom of infinity which says that beyond every term infinitely many are following. But don't bother and don't mourn. There are enough matheologians who will applaude if you recite that nonsense.)